WCT-Motivated GWTC Log-Domain Residual Diagnostic

This repository tests WCT-style log-domain residual structure in LIGO-Virgo-KAGRA Gravitational-Wave Transient Catalog (GWTC) event-catalog variables.

Scope and honesty statement

• It does not prove WCT.
• It does not replace LVK population-inference analyses.
• It does not claim a new gravitational-wave detection.
• Positive branches are treated as a candidate log-domain residual requiring independent confirmation and stronger source discrimination.

The repository separates descriptive structure, predictive holdout evidence, and source/null discrimination. A null-model result is evidence about a statistic under that declared null family; it is not automatically a causal explanation of the observed catalog.

Current evidence hierarchy

layer	current result	interpretation
Historical GWTC-4 aggregate	nominal 8.0522 sigma under an independent-uniform p-vector reference	Real descriptive nonuniformity, but the 168 scans are strongly dependent.
GWTC-4 dependence-aware N0-N3 nulls	empirical global 0.18-1.52 sigma for the historical aggregate statistic	The old 168-scan aggregate is not globally calibrated >5 sigma under those nulls; that does not establish a unique physical explanation.
Strict frozen holdout V1	p = 0.00129987, PASS_FIXED_MODE	Positive fixed-mode holdout evidence.
Unbinned KDE V3	Delta 2logL = 10.0122, 8/10000, p = 0.00089991, PASS_ROBUSTNESS_FIXED_MODE	The frozen mode survives removal of histogram binning and replacement of the polynomial baseline by a training-only KDE.
Structured non-periodic population-null V4	PASS_ALL_STRUCTURED_NULLS; worst-case p = 0.00559944	The exact frozen k = 9.7, amplitude and phase statistic is uncommon under all three declared non-periodic structured-population scenarios.

Publication figures

The publication-facing figure set is now kept in figures/publication/ and is generated from the committed frozen V2/V3/V4 artifacts rather than from the historical exploratory scan.

Regenerate the full SVG + PNG set with:

python scripts/make_publication_figures.py

Frozen-mode evidence hierarchy

V3 training-only frequency localization

V4 structured non-periodic null challenge

The figure directory also contains the strict holdout protocol, the V2 frozen model, and the V2/V3 cross-method frequency comparison. The historical figures/scan_M_chirp_B30.png remains preserved as exploratory/historical material and should not be used as the primary visual evidence for the strict k ~ 9.7 program.

V4 result

V4 was frozen before evaluation. The evaluator could not scan k, refit the residual coefficients, refit the structured population, or change the predeclared selection scenarios on the holdout.

Frozen signal:

• variable: M_chirp
• coordinate: ell = log(M_chirp)
• k = 9.7
• amplitude = 0.3853480195
• phase = 1.0982350915 rad
• holdout N = 104
• observed holdout Delta 2logL = 9.95018558

Declared non-periodic null family: continuous broken power law + truncated Gaussian peak, with selection weighting (Mchirp/Mchirp_max)^gamma for gamma = 0.0, 1.5, 2.5.

gamma	null >= observed	empirical p	verdict
0.0	55/10000	0.0055994401	PASS_STRUCTURED_NULL_SCENARIO
1.5	1/10000	0.0001999800	PASS_STRUCTURED_NULL_SCENARIO
2.5	2/10000	0.0002999700	PASS_STRUCTURED_NULL_SCENARIO

Overall verdict: PASS_ALL_STRUCTURED_NULLS.

This is a robustness/source-discrimination result, not an independent future-catalog replication, because GWTC-5 had already been inspected in earlier V2/V3 work. The V4 null is also phenomenological rather than a full LVK hierarchical population model with event-posterior propagation and injection-calibrated selection effects.

See:

• GWTC_V4_STRUCTURED_NULL_RESULT.md
• tables/gwtc_v4_frozen_structured_null.json
• tables/gwtc_v4_structured_null_result.csv
• V4_REPRODUCE.md

Why the historical 8.0522 sigma is kept separate

The restored historical analysis contains 168 scans = 56 subset selectors x 3 final-spin pairs. Its p-vector is strongly nonuniform under an independent-uniform reference, giving the literal nominal 8.0522 sigma calculation. That number is retained as a descriptive property of the historical scan ensemble.

However, N0-N3 whole-catalog dependence-aware calibrations give only about 0.18-1.52 sigma for that particular aggregate statistic. The correct conclusion is therefore narrow: the nominal 8.0522-sigma conversion is not a calibrated catalog-level significance for the dependent 168-scan architecture. It does not follow that the underlying structure has been causally explained away.

The newer V1/V3/V4 line was built to ask a different question: can a specific frozen phase/frequency/amplitude mode predict holdout data and survive progressively stronger non-periodic nulls?

Core hypothesis

If WCT-style curvature/winding structure appears in gravitational-wave catalogs, it should appear as stable residual phase organization in physically scale-like variables, not merely as arbitrary small p-values.

For a positive scale-like variable z, define ell = ln(z) and test a residual family

A cos(k ell - phi)

or equivalently

a cos(k ell) + b sin(k ell).

Exploratory scans may search k; stronger tests freeze k, amplitude, phase, baseline definition, and data split before evaluation.

Controls and interpretation

The repo retains negative control results, failed robustness branches, historical diagnostics, and model limitations. Bounded/non-scale variables such as |chi_eff| are diagnostic-only and cannot produce a primary physical PASS.

The strongest missing conventional challenge is now a posterior-aware hierarchical population/selection test using detector injections or an equivalent validated selection model while keeping the residual mode externally frozen. The strongest future evidentiary test is an independent future GWTC release evaluated once against a prediction frozen before release.

Data and reproduction

Source: official GWOSC Event API. Provenance is recorded in PROVENANCE.md and data/manifest.csv.

Key files:

• RESULTS.md — detailed evidence hierarchy and numerical results
• METHOD.md — definitions and verdict rules
• REPRODUCE.md — historical diagnostic reproduction
• V3_REPRODUCE.md — unbinned KDE fixed-mode robustness
• V4_REPRODUCE.md — frozen structured-population-null challenge
• GWTC_V4_STRUCTURED_NULL_RESULT.md — V4 result record
• figures/publication/README.md — publication figure index and paper placement guide
• scripts/make_publication_figures.py — regenerate publication SVG/PNG/PDF figures from committed artifacts
• TODO.md — remaining tests

Run the test suite with:

python -m pytest -q --basetemp=.pytest_tmp

This harness is deliberately designed to retain FAIL/PARTIAL outcomes and requires independent confirmation before stronger physical claims.